Palindromic gapful numbers: Difference between revisions
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8 : [808696968869696808]
9 : [968787783387787869]</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
This is among the faster versions of this problem. It solves the standard and optional tasks in 0.7 seconds.
<syntaxhighlight lang="Delphi">
{===========================================================}
function IsGapful(N: int64): boolean;
{Return true if number is "GapFul"}
{GapFul = combined first/last}
{ digits divide evenly into N}
var Digits: TIntegerDynArray;
var I: int64;
begin
Result:=False;
{Must be 3 digit number}
if N<100 then exit;
{Put digits in array}
GetDigits(N,Digits);
{Form number from first and last digit}
I:=Digits[0] + 10 * Digits[High(Digits)];
{Does it divide evenly into N}
Result:=(N mod I)=0;
end;
function HasEndDigit(N: int64; Digit: integer): boolean;
{Return true if last digit match specified "Digit"}
var LD: integer;
begin
LD:=N mod 10;
Result:=LD=Digit;
end;
function GetGapfulPalinEndSet(Max, EndDigit: integer): string;
{Get first Max number of Gapful Palindromes with specified EndDigit}
var I,Cnt,P: integer;
begin
Result:='Ending in: '+IntToStr(EndDigit)+CRLF;
Cnt:=0;
{Get palindromes and test them}
for I:=0 to high(Integer) do
begin
{Get next palinedrome}
P:=GetNthPalindrome(I);
{Is Gapful and has specified EndDigit}
if IsGapFul(P) and HasEndDigit(P,EndDigit) then
begin
Inc(Cnt);
{Display it}
Result:=Result+Format('%8d',[P]);
if (Cnt mod 5)=0 then Result:=Result+CRLF;
{Break when finished}
if Cnt>=Max then break;
end;
end;
end;
function LastGapfulPalinEndSet(Count,Last,EndDigit: integer): string;
{Get Gapful Palindromes with specified EndDigit}
{Get "Last" number of items out of a total "Count" }
var I,Inx: integer;
var P: int64;
var IA: TInt64DynArray;
begin
SetLength(IA,Count);
Result:='Ending in: '+IntToStr(EndDigit)+CRLF;
{Get count number of items}
Inx:=0;
for I:=0 to Count-1 do
begin
{Keep getting palindromes until}
{they Gapful and have specified last digit}
repeat
begin
P:=GetNthPalindrome(Inx);
Inc(Inx);
end
until IsGapFul(P) and HasEndDigit(P,EndDigit);
{Save item}
IA[I]:=P;
end;
{Get last items}
for I:=Count-Last to Count-1 do
begin
Result:=Result+Format('%12d',[IA[I]]);
if (I mod 5)=4 then Result:=Result+CRLF;
end;
end;
procedure ShowPalindromicGapfuls(Memo: TMemo);
var S: string;
begin
Memo.Lines.Add('First 20 palindromic gapful numbers');
Memo.Lines.Add(GetGapFulPalinEndSet(20,1));
Memo.Lines.Add(GetGapFulPalinEndSet(20,2));
Memo.Lines.Add(GetGapFulPalinEndSet(20,3));
Memo.Lines.Add(GetGapFulPalinEndSet(20,4));
Memo.Lines.Add(GetGapFulPalinEndSet(20,5));
Memo.Lines.Add(GetGapFulPalinEndSet(20,6));
Memo.Lines.Add(GetGapFulPalinEndSet(20,7));
Memo.Lines.Add(GetGapFulPalinEndSet(20,8));
Memo.Lines.Add(GetGapFulPalinEndSet(20,9));
Memo.Lines.Add('86th to 100th');
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,1));
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,2));
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,3));
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,4));
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,5));
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,6));
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,7));
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,8));
Memo.Lines.Add(LastGapFulPalinEndSet(100,15,9));
Memo.Lines.Add('991st to 1000th:');
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,1));
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,2));
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,3));
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,4));
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,5));
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,6));
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,7));
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,8));
Memo.Lines.Add(LastGapFulPalinEndSet(1000,10,9));
end;
</syntaxhighlight>
{{out}}
<pre>
First 20 palindromic gapful numbers
Ending in: 1
121 1001 1111 1221 1331
1441 1551 1661 1771 1881
1991 10901 11011 12221 13431
14641 15851 17171 18381 19591
Ending in: 2
242 2002 2112 2222 2332
2442 2552 2662 2772 2882
2992 20702 21912 22022 23232
24442 25652 26862 28182 29392
Ending in: 3
363 3003 3333 3663 3993
31713 33033 36663 300003 303303
306603 309903 312213 315513 318813
321123 324423 327723 330033 333333
Ending in: 4
484 4004 4224 4444 4664
4884 40304 42724 44044 46464
48884 400004 401104 402204 403304
404404 405504 406604 407704 408804
Ending in: 5
5005 5115 5225 5335 5445
5555 5665 5775 5885 5995
50105 51315 52525 53735 54945
55055 56265 57475 58685 59895
Ending in: 6
6006 6336 6666 6996 61116
64746 66066 69696 600006 603306
606606 609906 612216 615516 618816
621126 624426 627726 630036 633336
Ending in: 7
7007 7777 77077 700007 707707
710017 717717 720027 727727 730037
737737 740047 747747 750057 757757
760067 767767 770077 777777 780087
Ending in: 8
8008 8448 8888 80608 86768
88088 800008 802208 804408 806608
808808 821128 823328 825528 827728
829928 840048 842248 844448 846648
Ending in: 9
9009 9999 94149 99099 900009
909909 918819 927729 936639 945549
954459 963369 972279 981189 990099
999999 9459549 9508059 9557559 9606069
86th to 100th
Ending in: 1
165561 166661 167761 168861 169961
170071 171171 172271 173371 174471
175571 176671 177771 178871 179971
Ending in: 2
265562 266662 267762 268862 269962
270072 271172 272272 273372 274472
275572 276672 277772 278872 279972
Ending in: 3
30366303 30399303 30422403 30455403 30488403
30511503 30544503 30577503 30600603 30633603
30666603 30699603 30722703 30755703 30788703
Ending in: 4
4473744 4485844 4497944 4607064 4619164
4620264 4632364 4644464 4656564 4668664
4681864 4693964 4803084 4815184 4827284
Ending in: 5
565565 566665 567765 568865 569965
570075 571175 572275 573375 574475
575575 576675 577775 578875 579975
Ending in: 6
60399306 60422406 60455406 60488406 60511506
60544506 60577506 60600606 60633606 60666606
60699606 60722706 60755706 60788706 60811806
Ending in: 7
72299227 72322327 72399327 72422427 72499427
72522527 72599527 72622627 72699627 72722727
72799727 72822827 72899827 72922927 72999927
Ending in: 8
80611608 80622608 80633608 80644608 80655608
80666608 80677608 80688608 80699608 80800808
80811808 80822808 80833808 80844808 80855808
Ending in: 9
95311359 95400459 95499459 95588559 95677659
95766759 95855859 95944959 96033069 96122169
96211269 96300369 96399369 96488469 96577569
991st to 1000th:
Ending in: 1
17799771 17800871 17811871 17822871 17833871
17844871 17855871 17866871 17877871 17888871
Ending in: 2
27799772 27800872 27811872 27822872 27833872
27844872 27855872 27866872 27877872 27888872
Ending in: 3
3084004803 3084334803 3084664803 3084994803 3085225803
3085555803 3085885803 3086116803 3086446803 3086776803
Ending in: 4
482282284 482414284 482535284 482656284 482777284
482898284 482909284 483020384 483141384 483262384
Ending in: 5
57800875 57811875 57822875 57833875 57844875
57855875 57866875 57877875 57888875 57899875
Ending in: 6
6084004806 6084334806 6084664806 6084994806 6085225806
6085555806 6085885806 6086116806 6086446806 6086776806
Ending in: 7
7452992547 7453223547 7453993547 7454224547 7454994547
7455225547 7455995547 7456226547 7456996547 7457227547
Ending in: 8
8085995808 8086006808 8086116808 8086226808 8086336808
8086446808 8086556808 8086666808 8086776808 8086886808
Ending in: 9
9675005769 9675995769 9676886769 9677777769 9678668769
9679559769 9680440869 9681331869 9682222869 9683113869
Elapsed Time: 763.788 ms.
</pre>
===Translation of F#===
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